
\(f^L_d(\cdot ,\cdot )\)  belongs to the family of decomposition functions in (REF ),  i.e., for each \(i \in \mathbb {N}_{n_x}\) , a specific pair of \(\mathbf {m}_i^L \in \mathbf {M}_i\)  and \(h_i^L(\cdot ) \in \mathcal {H}_{\mathbf {M}_i}\)  corresponds to the decomposition function \(f^L_d(\cdot ,\cdot )\)  in [1]} (cf. Proposition REF ).

The optimal remainder-form decomposition function \(T^f_{R}\)  is always tighter than (at least as good as) the inclusion function \(T^f_L\) , induced by the decomposition function \(f^L_d\) .


